Banach空间中的平均非扩张映象:不动点的存在定理

<正> 设X是Banach空间,E是X中的集合,T是映集合E到自身的映象.若T满足条件(称为平均非扩张条件)其中x,y∈E,a,b,c≥0且a+2b+2c≤1,则称T是平均非扩张映象. 文[1]概括了近年来研究关于平均非扩张映象不动点的一些主要结果.本文进     

Elliptic curves and their torsion subgroups over number fields of type (2, 2,

Suppose that E：y2=x(x+M)(x+N) is an elliptic curve, where M相似文献   

积分算子的n-逼近数

本文研究了积分算子ＴＫ：Ｌｑ［０，１］→Ｌｑ［０，１］，（ｑ≥１）当核 Ｋ（ｓ， ｔ）是 Ｓｏｂｏｌｅｖ空间 Ｗｐｒ（［０， １］２）中元素时ｎ－逼近数 ａｎ（ＴＫ： Ｌｑ→ Ｌｑ）的估计，并把这个估计应用于退化核方法解第二类线性Ｆｒｅｄｈｏｌｍ方程（Ｉ一ＴＫ）ｘ＝ｙ时，Ｂａｄｈｖａｌｏｖ［５］意义下最佳误差的讨论中，所得到的最佳误差之估计当ｑ＝１时，最优化了［１０］的结论．     

有限个严格压缩映像隐迭代格式的逼近

假设E为一致凸的Banach空间,对偶空间E*有Kadec-Klee性质,K为E的非空闭凸子集{Ti:i=1,2,…,N}:K→K为Browder-Petryshyn意义下的严格伪压缩映像且F=∩Ni=1F(Ti)≠0.{αn}n∞=1满足0相似文献   

On intersections of independent anisotropic Gaussian random fields

Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where  is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.     

Algebraic morphisms into grassmannians:differential geometry and frobenius

Let Xbe a projective variety (over Spec(K)) and f:X→G(r,v) a morphism to a Grassmannian, i.e. a pair (E,V) where E is a rank r vector bundle on V?H^O(X,E) is a subspace spanning E with dim(V) = v. Here we study the differential properties of f and their relations to a sequence of quotient bundles E→E₁→E₂→of E called the derived bundles of (E,V). In the first 5 sections we study the case X a smooth curve, char(K) >0 (the case char(K) = 0, being due to D. Perkinson). Then we give a general duality theorem for the derived bundles when Xis any normal variety.     

Permanence properties of C(X,E)

Let C(X,E) be the vector space of all continuous functions on a completely regular Hausdorff space X with values in a locally convex space E, equipped with the compact-open topology. In this note it will be shown that for many classes of locally convex spaces K C(X,E) lies in K if and only if C(X)=C(X,¦K) (¦K=¦R or C) and E belong to K. This is valid for the classes K. of all metrizable, normed, (DF)-, -locally topological, separable, quasi-complete, complete, nuclear, Schwartz, semi-Montel, Montel, semi-reflexive, reflexive and quasi-normable locally convex spaces, respectively. But in general C(X,E) is not quasi-barrelled, barrelled and bornological, respectively, if C(X) and E belong to the same class. We shall give sufficient conditions for C(X,E) to be quasi-barrelled and barrelled, respectively.Herrn Professor Gottfried Köthe zum 75. Geburtstag gewidmet     

Strong Convergence of the Kernel Estimates of Nonparametric Regression Functions

Let (X, Y), (X_1, Y_1),\cdots, (X_n, Y_n) be i. i. d. random vectors taking values in R_d\times R with E(|Y|)<\infinity, To estimate the regression function m(x)=E(Y|X=x), we use the kernel estimate $m_n(x)=[\sum\limits_{i = 1}^n {K(\frac{{{X_i} - x}}{{{h_n}}}){Y_i}/} \sum\limits_{i = 1}^n {K(\frac{{{X_j} - x}}{{{h_n}}})} \]$ where K(x) is a kernel function and h_n a window width. In this paper, we establish the strong consistency of m_n(x) when E(|Y|^p)<\infinity for some p>l or E{exp(t|Y|^\lambda)}<\infinity for some \lambda>0 and t>0. It is remakable that other conditions imposed here are independent of the distribution of (X, Y).     

迭代逼近m-增生映象的零点

设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设A是m-增生映象,使得C=■是E的凸子集,数列{α_n)■[0,1],{r_n}■ (0,∞),在适当的条件下,则由(1.2)式定义的迭代序列{x_n}强收敛于A~(-1)(0)中的点.其次证明了:设E是一致凸Banach空间,其范数是Frechet可微的.设数列{α_n},{β_n)■(0,1),{r_n}■(0,∞),满足适当的条件.如果A~(-1)(0)∩B~(-1)(0)≠φ,则由(3.20)式定义的序列{x_n}弱收敛于A~(-1)(0)∩B~(-1)(0)中的点.其结果推广和改进了Kamimura,Takahashi(2000)的定理2及Xu H.K.(2006)的定理4.1,定理4.2和定理4.3:(i)Kamimura,Takahashi(2000)定理2中的假设"自反Banach空间E的每个有界闭凸子集对非扩张自映象有不动点性质"被去掉;(ii)Xu H.K.(2006)的假设"E是具有弱连续对偶映象J_φ的自反Banach空间",被本文的假设"E是具有一致正规结构且其范数是一致Gateaux可微的Banach空间"所取代.从而补充了Xu H.K.(2006)未包含的另外一些Banach空间.同时还证明了逼近两个m-增生映象的公共零点,其结果也推广和改进了Mainge的相应结果.     

Banach空间中一类混合映射不动点的Ishikawa迭代逼近问题

设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为Φ-强伪压缩映射.其中T=T1+T2,T1:K→K为Lipschitz映射,T2:K→K为具有有界值域映射.设{αn}n∞=0和{βn}n∞=0是[0,1]中满足一定条件的两实数列.则Ishikawa迭代序列{xn}∞n=0强收敛于T的唯一不动点.     

CD0(K,E) and CDω(K,E)-Spaces as Banach Lattices

Banach lattices CD ₀(K,E) and CD (K,E) are introduced and lattice-norm properties of these spaces are investigated. We identify the centre and order continuous dual of these spaces.     

Measures on spaces of operators and isometries

One considers a question that arises at the investigation of isometric operators in vector-valued L^p -spaces. Let E, F be Banach spaces, let p>0, let μ be a probability Borel measure on the space on continuous linear operators from E into F such that for any e ε E one has $$\left\| e \right\|^p = \int {\left\| {Te} \right\|^p } d\mu \left( T \right)$$ . In the cases when: 1) E=C(K), K is a metric compactum, F is an arbitrary space, p>1 and 2) 2)E=F=L^q,p>1, q>1 q ?[p,2] it is Proved that the support of the measure μ is contained in the set of the operators that are scalar multiples of isometries. For E=C(K) one obtains an isomorphic analogue of this result: if the Banach-Mazur distance between C(K) and the P -sum of Banach spaces is small, then the distance between C(K) and one of the spaces is small.     

Generalizations of vector quasivariational inclusion problems with set-valued maps

Existence theorems are given for the problem of finding a point (z ₀,x ₀) of a set E × K such that and, for all where α is a relation on 2 ^Y (i.e., a subset of 2 ^Y  × 2 ^Y ), and are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of α and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.     

Effective p-descent

Given E, an elliptic curve defined over K, a field of positive characteristic, provided that j, the Weierstrass j-invariant, is not an element of Kp, we construct explicitly, that is, we give by a closed form formula, a non-trivial homomorphism, :E(K) K+, from the group of K-rational points of E to K+, the additive group of K. In the course of our analysis we discover a canonical differential, , associated to E and we relate it to the differential dq/q associated to the Tate curve. If the transcendence degree of K over is equal to one, as for example is the case for function fields in one variable, then is a p-descent map, that is, its kernel is equal to pE(K) and the explicit formula for can be used to provide effective proofs of analogues of classical theorems on elliptic curves. For example, in the author's thesis at The University of Texas at Austin the analogue of Siegel's Theorem on the finiteness of integral points of E(K) is proved effectively.     

Lifting Automorphisms

Let A be a unital nuclear separable C*-algebra which satisfies the Universal Coefficient Theorem and E be a unital essential extension of the form:

Über kompakte Operatoren in lokalkonvexen Räumen

Let E, F be (B)-spaces and let E have the approximation property. Then the closure of FE in L_b (F,E) is identical with the space K(F,E) of compact maps in L(F,E). The following generalization of this well known statement is proved: Let E, F be complete, locally convex spaces and let E have the approximation property. Then, where denotes a 0-neighborhood base in F and refers to the completion of the tensor product with respect to the topology of bi-equicontinuous convergence.The last part is concerned with the adjoint map of a compact operator.     

Injectivity of the Petri map for twisted Brill–Noether loci

Let C be a generic curve, E a generic vector bundle on C. Then, for every line bundle on C the twisted Petri map $$P_{E}:H^0(C,L\otimes E)\otimes H^0(C, K\otimes L^*\otimes E^{*})\rightarrow H^0(C, K)$$ is injective.     

Asymptotic behavior of interior transition layers for nonlinear boundary-value problem with small parameter

The system of equations

连续伪压缩映射的黏滞迭代逼近方法

设K是实自反Banach空间E的一个闭凸子集,T：K→K是一个连续伪压缩映射,f：K→K是一个固定的L-Lipschitzian强伪压缩映射．对于任意的t∈(0,1),设x_t是tf+(1-t)T的唯一不动点．我们证明了如果T有不动点且有从E到E~*弱序列连续对偶映像,则当t趋于0时,{x_t}收敛于T的一个不动点．这个结果改进和推广了文[4]的相应结果．     

具误差隐格式迭代逼近严格伪压缩映像族公共不动点

设K是实Banach空间E中非空闭凸集, {Ti}i=1N是N个具公共不动点集F的严格伪压缩映像, {an}(?)[0,1]是实数列, {un}(?)K是序列,且满足下面条件设X0∈K,{xn}由下式定义xn=αnxn-1 (1-αn)Tnxn-un-1,n≥1其中Tn=TnmodN,则有下面结论(i)limn→∞‖xn-p‖存在,对所有P∈F; (ii)limn→∞d(xn,F)存在,当d(xn,F)=infp∈F‖xn-p‖; (iii)liminfn→∞‖xn-Tnxn‖=0．文中另一个结果是,如果{xn}(?){1-2-n,1},则{xn}收敛．文中结果改进与扩展了Osilike(2004)最近的结果,证明方法也不同．